Solve for $x$ and $y$ using elimination. ${-3x-y = -14}$ ${-5x-y = -22}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-3x-y = -14}$ $5x+y = 22$ Add the top and bottom equations together. $2x = 8$ $\dfrac{2x}{{2}} = \dfrac{8}{{2}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-3x-y = -14}\thinspace$ to find $y$ ${-3}{(4)}{ - y = -14}$ $-12-y = -14$ $-12{+12} - y = -14{+12}$ $-y = -2$ $\dfrac{-y}{{-1}} = \dfrac{-2}{{-1}}$ ${y = 2}$ You can also plug ${x = 4}$ into $\thinspace {-5x-y = -22}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - y = -22}$ ${y = 2}$